Phonon MC simulation

In phonon MC simulations, the movement and scattering of individual phonons are tracked to yield a statistical description of the transport process, as an alternative way to solve the phonon BTE. By employing the periodic heat flux boundary condition (Hao et al., 2009; Hao and Xiao, 2020), a single period can be selected as the computational domain to minimize the computational load. The computational efficiency can be further improved using a variance-reduced MC technique developed by Péraud and Hadjiconstantinou, where the tracked “useful” phonons are related to the distribution function distortion from an equilibrium distribution function, i.e., the Bose-Einstein distribution at a reference temperature (Péraud and Hadjiconstantinou, 2011). These tracked phonons are directly associated with the net heat flow across a structure. Phonon boundary scattering and internal scattering are two scattering events in the simulation. The former includes scattering with the nanoslot edge and top/bottom film surfaces, which are both treated as diffusive. Considering impurity scattering and Umklapp (U) scattering, the internal phonon scattering rate is expressed as 1/τ(ω)=A1ω4+B1ω2Texp(−B2/T). In the expression, τ(ω) is the phonon relaxation time depending on the phonon angular frequency ω, A₁ is the parameter for the impurity scattering, B₁ and B₂ are the parameters for the U processes. The employed parameters were obtained by fitting the temperature-dependent k_L of bulk Si (Hao, 2014; Wang et al., 2011). Following these works, A1=1.69×10−45s3, B1=1.53×10−19s/K and B2=140K were used in the simulation of undoped samples. For samples with point defects introduced by the ion implantation, the A₁ value should be further increased to account for stronger point-defect phonon scattering (Hao et al., 2010).